MinT - Information on Result #705840

Information on Result #705840

Linear OA(3²⁴⁸, 771, F₃, 62) (dual of [771, 523, 63]-code), using constructionÂ XX applied to C₁Â =Â C([337,394]), C₂Â =Â C([333,388]), C₃Â =Â C₁Â +Â C₂Â =Â C([337,388]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([333,394]) based on

linear OA(3²²⁰, 728, F₃, 58) (dual of [728, 508, 59]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,394}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 59 [i]
linear OA(3²²⁰, 728, F₃, 56) (dual of [728, 508, 57]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {333,334,…,388}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 57 [i]
linear OA(3²³⁵, 728, F₃, 62) (dual of [728, 493, 63]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {333,334,…,394}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 63 [i]
linear OA(3²⁰⁵, 728, F₃, 52) (dual of [728, 523, 53]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,388}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 53 [i]
linear OA(3⁸, 23, F₃, 5) (dual of [23, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁸, 26, F₃, 5) (dual of [26, 18, 6]-code), using
  - dual code (with bound on d by constructionÂ Y1) [i] based on
    1. linear OA(3¹⁸, 26, F₃, 12) (dual of [26, 8, 13]-code), using
      - 2 times truncation [i] based on linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
    2. nonexistence of linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), because
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
- doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
  - ovoid in PG(3,Â 3) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴⁸, 385, F₃, 2, 62) (dual of [(385, 2), 522, 63]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴⁸, 257, F₃, 3, 62) (dual of [(257, 3), 523, 63]-NRT-code)	[i]		OOA Folding